A shopkeeper allows a discount of 12.5% on the marked price of a certain article and makes a profit of 20%. If the article costs the shopkeeper Rs 210, then the marked price of the article will be

Options

A. Rs 387
B. Rs 350
C. Rs 386
D. Rs 288

Answer

To find the marked price of the article, we can follow these steps:

### Step 1: Understand the relationship between Cost Price (CP), Selling Price (SP), and Marked Price (MP)
- The shopkeeper allows a discount on the marked price and sells the article at a selling price that gives him a profit over the cost price.
- The profit percentage is given, which helps us find the selling price.

### Step 2: Calculate the Selling Price (SP)
- The cost price (CP) of the article is Rs 210.
- The profit percentage is 20%.
- To calculate the selling price (SP), we use the formula:

\[ SP = CP + (Profit \% \times CP) \]

- Plugging in the values:

\[ SP = 210 + (20\% \times 210) = 210 + (0.20 \times 210) = 210 + 42 = 252 \]

### Step 3: Relate Selling Price to Marked Price using Discount
- The shopkeeper gives a discount of 12.5% on the marked price (MP).
- The selling price (SP) can also be expressed in terms of the marked price after applying the discount:

\[ SP = MP - (Discount \% \times MP) \]

- This can be rewritten as:

\[ SP = MP \times (1 - \text{Discount \%}) \]

- Plugging in the discount percentage:

\[ SP = MP \times (1 - 0.125) = MP \times 0.875 \]

### Step 4: Set the two expressions for SP equal to each other
- Now we can set the two expressions for SP equal to each other:

\[ 252 = MP \times 0.875 \]

### Step 5: Solve for Marked Price (MP)
- To find the marked price, rearrange the equation:

\[ MP = \frac{252}{0.875} \]

- Calculating the value:

\[ MP = 288 \]

### Conclusion
- The marked price of the article is Rs 288.

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